THE JOURNAL OF CHEMICAL PHYSICS 128, 024307 共2008兲
Mode selective photodissociation dynamics in V+„OCO…
Murat Citir and Ricardo B. Metza兲
Department of Chemistry, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA
共Received 23 October 2006; accepted 5 November 2007; published online 11 January 2008兲
The electrostatic V+共OCO兲 complex has a vibrationally resolved photodissociation spectrum in the
visible. Photodissociation produces V+ + CO2 共nonreactive pathway兲 and VO+ + CO 共reactive
pathway兲. Production of VO+ is energetically favored, but spin forbidden. One-photon dissociation
studies confirm mode selectivity observed by Lessen et al. 关J. Chem. Phys. 95, 1414 共1991兲兴:
excitation of one quantum of rocking motion enhances VO+ production by ⬎30%. Branching ratio
measurements in one-photon dissociation are extended to higher energy. The effect of OCO
antisymmetric stretch vibrations on reactivity is investigated using vibrationally mediated
photodissociation, in which the OCO antisymmetric stretch is excited at 2390.9 cm−1. Vibrationally
excited molecules are then dissociated in the visible. Seven vibronic bands are investigated,
involving the antisymmetric stretch alone and in combination with the CO2 bend, the V+共OCO兲
stretch and rock. Exciting the antisymmetric stretch leads to a ⬃15% increase in the reactive VO+
channel, compared to other states at similar energy. Combination bands involving the antisymmetric
stretch all show slightly higher reactivity. Electronic structure calculations were performed to
characterize the dissociation pathways and excited electronic states of V+共OCO兲. The geometries of
reactants, products, and transition states and relative energies of quintet and triplet states were
determined using hybrid density functional theory; energies were also calculated using the coupled
cluster with single, double and perturbative triple excitations method. In addition, time-dependent
density functional theory calculations were performed to predict the excited electronic states of
quintet and triplet V+共OCO兲. Spin-orbit coupling of quintet states to triplet states was calculated and
used to compute intersystem crossing rates, which reproduce many of the observed mode selective
trends. The V+ – OCO stretch and OCO antisymmetric stretch appear to enhance reactivity by
increasing the intersystem crossing rate. © 2008 American Institute of Physics.
关DOI: 10.1063/1.2818564兴
INTRODUCTION
Influencing the course of a reaction to promote a desired
product channel is a long-standing goal of chemistry. Compared to a bimolecular reaction, photoinitiating the reaction
from an isolated, weakly bound reactant cluster provides
greater control over the reaction, as reactant orientation, angular momentum, and energy are constrained. In addition,
specific vibrational motions in the cluster can be photoexcited and any chemistry dependent on this motion revealed.
During the path of a branched reaction the species involved
must at some point along the reaction coordinate “choose”
which path to follow. If at or near this decision point the
complex is selectively excited along a particular vibrational
mode, the branching ratios for the reaction may change. Control of ion-molecule reactions is experimentally attractive because the reactant complex is much more strongly bound
than neutral van der Waals complexes and because the products and their branching ratio can readily be measured using
mass spectrometry. If we can identify and excite a vibration
in 关MAB兴+* that corresponds to the desired motion, then we
a兲
Author to whom correspondence should be addressed. Electronic mail:
rbmetz@chemistry.umass.edu.
0021-9606/2008/128共2兲/024307/10/$23.00
may be able to control the products of the corresponding
M+* + AB reaction, influencing the relative production of
MA+ + B and MB+ + A,
V+共OCO兲 is a particularly interesting system in which to
investigate mode selectivity, as it is a small molecule with
two chemically district pathways at similar energies,
V+ forms a linear, electrostatic complex with CO2, and
V 共OCO兲 is calculated to have a 5兺 or 5⌬ ground state.1,2
Vibrational spectroscopy confirms that V+共OCO兲 is linear.1
Dissociation via the reactive pathway 共2b兲 is energetically
favored, but is spin forbidden. Lessen et al. obtained a vibrationally resolved photodissociation spectrum of V+共OCO兲 in
the visible region.3 Dissociation occurs through both the reactive 共2b兲 and nonreactive 共2a兲 channels. They observed an
+
128, 024307-1
© 2008 American Institute of Physics
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J. Chem. Phys. 128, 024307 共2008兲
M. Citir and R. B. Metz
interesting mode selectivity. The VO+ / V+ branching ratios
for states with no vibrational excitation in the electronically
excited V+共OCO兲 and excitation of one quantum of
V+共OCO兲 stretch or CO2 bend are identical. However, excitation of one quantum of the rocking motion enhances the
relative VO+ production by 50%.
In a simple, collinear picture, the reaction coordinate for
the reactive channel should be similar to the OCO antisymmetric stretch vibration. So, exciting this vibration should
also enhance reactivity, but progressions in this stretch were
not observed in the spectrum, due to small Franck-Condon
factors. Recently, we measured the OCO antisymmetric
stretch frequency in the ground electronic state of V+共OCO兲
␯1⬙ = 2392 cm−1
using
vibrationally
mediated
photodissociation.1 In this work, we use vibrationally mediated photodissociation 共VMP兲 to study how the OCO antisymmetric stretch and combinations of antisymmetric stretch
with other vibrations affect the mode selectivity of reaction
2. IR absorption prepares molecules with one quantum of
antisymmetric OCO stretch. A visible photon promotes the
molecules to a predissociative electronic state, with one
quantum of OCO antisymmetric stretch excitation, alone or
in combination with the V+-共OCO兲 stretch and rock, and the
CO2 bend.
EXPERIMENTAL APPROACH
Vibrationally mediated photodissociation of V+共OCO兲
was studied on a dual time-of-flight reflectron photofragment
spectrometer which has been described in detail
previously.4,5 Vanadium cations are produced in a standard
laser ablation source. The frequency-doubled output of a
pulsed Nd:YAG 共YAG denotes yttrium aluminum garnet兲 laser operating at 20 Hz repetition rate is loosely focused onto
a rotating and translating vanadium rod 共Sigma-Aldrich,
99.98% pure兲. Ablated V+ ions react with a gas mixture of
⬃0.08% carbon dioxide 共99.98% pure兲 in helium 共99.98%
pure兲 to produce V+共OCO兲n. Ions produced in the source
undergo supersonic expansion into vacuum, producing electronically and vibrationally cold ions with rotational temperatures of ⬃12 K.1 The molecular beam is skimmed, and
ions are extracted along the beam axis using a pulsed electric
field, accelerated to 1800 V kinetic energy and rereferenced
to ground potential prior to entering the time-of-flight mass
spectrometer. Ions are photodissociated at the turning point
of the reflectron. Fragment ions are detected by a dual
40 mm dia. microchannel plate detector and the signal is
amplified and collected using a 500 MHz digital oscilloscope. Fragment ions and their branching ratios are measured
using difference spectra, the difference between time-offlight spectra obtained with the laser unblocked and blocked.
Photodissociation spectra are obtained by measuring signal
in a particular fragment ion channel as a function of wavelength using a gated integrator and normalizing to parent ion
signal and laser power.
In the VMP studies, ions are vibrationally excited with
an IR laser. A visible laser then promotes vibrationally excited molecules to a predissociative excited electronic state.
An IR optical parametric oscillator/optical parametric ampli-
FIG. 1. Difference spectra obtained from photodissociation of V+共OCO兲 共a兲
in the near-IR band at 7300 cm−1, 共b兲 at the origin of the visible band
共15801 cm−1兲, and 共c兲 from molecules with one quantum of OCO antisymmetric stretch vibration in the excited electronic state, produced by exciting
the antisymmetric stretch ␯1 at 2390.9 cm−1, then the 111 band at
15 777.1 cm−1. Figure 1共c兲 has been multiplied by a factor of 4.
fier 共OPO/OPA兲 共Laser Vision兲 pumped by an injectionseeded Nd:YAG laser produces light in the midinfrared region. The IR laser system uses a combination of a 532 nm
pumped OPO and a 1064 nm pumped OPA. It is tunable
from 2100 to⬎ 4000 cm−1 in the mid-IR, producing
3 mJ/pulse near 2400 cm−1, with 0.2 cm−1 linewidth. It also
produces 3 – 9 mJ/pulse from 6050– 7425 cm−1 in the near
IR. The visible laser system is a Nd:YAG pumped dye laser
共Continuum兲 with ⬍0.08 cm−1 linewidth. The mid-IR laser
wavelengths are calibrated using the photoacoustic spectrum
of methane.6 The dye laser is calibrated using the absorption
spectrum of I2.7 The delay between the IR and visible lasers
is ⬃40 ns.
RESULTS
One-photon dissociation
In the near IR, V+共OCO兲 has a complex photodissociation spectrum.1 Throughout this region, photodissociation
occurs solely via production of V+ 共nonreactive channel兲, as
shown in Fig. 1共a兲. V+共OCO兲 has a second absorption band
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024307-3
Mode selective photodissociation dynamics
J. Chem. Phys. 128, 024307 共2008兲
FIG. 2. 共Color online兲 Photodissociation spectrum of V+共OCO兲, with assignments 共black兲. Insets and assignments in red show the photodissociation spectrum
of molecules excited with one quantum of OCO antisymmetric stretch, ␯⬙1 at 2390.9 cm−1. Their intensities have been multiplied by a factor of 2. The shifts
show that ␯⬘1 共excited state兲 lies ⬃24 cm−1 below ␯⬙1 共ground state兲, and that there is a small amount of vibrational cross anharmonicity.
in the visible region, with sharp, well resolved vibronic features. Photodissociation in this band leads to production of
both V+ and VO+, as shown in Fig. 1共b兲.
Figure 2 shows the photodissociation spectrum of
V+共OCO兲 in the visible region. This spectrum was previously observed by Lessen et al.3 The origin lies at
15 801 cm−1. There are progressions in several excited state
vibrations, the V+-共OCO兲 stretch 共␯3⬘ = 186 cm−1兲, the OCO
bend 共␯4⬘ = 597 cm−1兲, and the V+-共OCO兲 rock 共␯5⬘
= 105 cm−1兲, all in agreement with the earlier study.3 We also
observe a weak transition due to the OCO symmetric stretch,
which gives ␯2⬘ = 1340 cm−1. Using vibrationally mediated
photodissociation, we previously1 measured the OCO antisymmetric stretch ␯1⬘ = 2368 cm−1, so all vibrational frequencies in the excited electronic state of V+共OCO兲 have been
measured. Using difference spectra, we determine the
branching ratio of the reactive VO+ channel to the nonreac-
tive V+ channel at 51 vibronic peaks in the visible band.
These measure the influence of the V+-共OCO兲 stretch and
rock, CO2 bend, and combinations of these motions, on the
dissociation pathway. The results are shown in Fig. 3. Detailed results and assignments are in Table S1 of Ref. 8. Our
results on the branching ratios generally agree with those
previously obtained by Lessen et al. One quantum of
V+-共OCO兲 rock 共␯5⬘兲 enhances the reactive channel, while
one quantum of V+-共OCO兲 stretch 共␯3⬘兲 or CO2 bend 共␯4⬘兲
slightly decreases it. We also find significant enhancement
共⬃70% 兲 of reactivity when exciting 3␯3⬘ + ␯5⬘ which lies only
50 cm−1 above ␯4⬘, a result that was not reported earlier, presumably due to the low total photodissociation cross section
for this peak. Overall, reactivity for one-photon dissociation
generally increases with energy, up to energies of
⬃17 000 cm−1 and a VO+ / V+ ratio of ⬃0.95, then slightly
decreases at higher energy.
FIG. 3. Mode selectivity in photodissociation of
V+共OCO兲. The ratio of the reactive 共VO+ + CO兲 to nonreactive 共V+ + CO2兲 product is measured at the peaks of
the vibronic bands shown in Fig. 2. The diamonds show
bands accessed by one-photon excitation, data obtained
by vibrationally mediated photodissociation exciting
the OCO antisymmetric stretch is shown in circles.
Filled symbols correspond to assigned peaks 共assignments in Fig. 2 and Table S1兲.
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024307-4
M. Citir and R. B. Metz
Vibrationally mediated photodissociation
We recently measured the OCO antisymmetric stretch
frequency ␯1⬙ in the ground electronic state of V+共OCO兲 using two techniques: photodissociation depletion spectroscopy
and vibrationally mediated photodissociation.1 We find ␯1⬙
= 2392 cm−1, which is 43 cm−1 blueshifted from the value in
isolated CO2. Setting the IR laser to the peak of the P branch
of the ␯1 band at 2390.9 cm−1 and tuning the visible laser in
the vicinity of the vibronic origin band reveals a new peak at
15 777 cm−1 共Fig. 2兲. This peak is due to the ␯1⬘ = 1 ← ␯1⬙ = 1
sequence band. The 24 cm−1 shift to the red of the origin
gives ␯1⬘ = 2392− 24= 2368 cm−1.
In general, VMP experiments have been used to measure
the spectroscopy of regions of the potential energy surface of
the excited state that are not Franck-Condon accessible from
the ground state and to show how different vibrations affect
the photodissociation dynamics.9–12 In this case, IR excitation of the OCO antisymmetric stretch 共␯1⬙兲 allows us to access excited state vibronic bands with ␯1⬘ = 1 and to measure
how antisymmetric stretch excitation affects the dissociation
dynamics. Figure 1共c兲 shows the difference mass spectrum
obtained after exciting the ␯1⬘ = 1 ← ␯1⬙ = 1 band. This was obtained by taking the difference between time-of-flight mass
spectra with the IR laser blocked and unblocked. The visible
laser was always unblocked. Uncertainties in the VO+ / V+
branching ratio are larger in the VMP experiments than in the
one-photon measurements, as the total fragment signal is
smaller, and there is always fragment signal from the visible
laser alone. Comparison of Figs. 1共b兲 and 1共c兲 clearly shows
that antisymmetric stretch excitation enhances the yield of
the reactive VO+ product.
We excited several different combination bands involving the OCO antisymmetric stretch, as shown in Fig. 2. At
each peak, we measured the relative amounts of reactive
共VO+兲 and unreactive 共V+兲 products produced by photodissociation of V+共OCO兲. Our experimental results are summarized in Fig. 3 共filled circles兲 and in Table S1 of Ref. 8.
Exciting the OCO antisymmetric stretch enhances the VO+
yield by almost a factor of 3, compared to the yield for the
ground vibrational state. Exciting combination bands of antisymmetric stretch with several other vibrations increases
the VO+ yield a bit more, but combination bands involving
the antisymmetric stretch all give similar branching ratios.
Excitation of the antisymmetric stretch slightly enhances the
reactivity, even when compared with other vibrational states
at similar energy. Figure 3 shows that, above ⬃17 000 cm−1
the branching ratio for states accessed by one-photon excitation reaches a plateau at ⬃0.9 and may decrease slightly at
higher energy. Compared to this value, states produced by
vibrationally mediated photodissociation exciting the OCO
antisymmetric stretch show enhanced reactivity of ⬃15% for
␯1⬘ and ⬃25% for combination bands involving ␯1⬘.
Electronic structure calculations
To characterize V+共OCO兲, its excited electronic states,
and dissociation pathways we did three types of calculations.
We first calculated the geometries and relative energies of
quintet and triplet V+共OCO兲 and OV+CO and the transition
J. Chem. Phys. 128, 024307 共2008兲
state connecting them. We then calculated excited electronic
states of quintet and triplet V+共OCO兲. Finally, we calculated
the spin-orbit coupling between the quintet and triplet states.
Density functional theory is used for geometry optimization and frequency calculations. All geometries are optimized using Becke’s three-parameter hybrid functional13
combined with the Lee, Yang, and Parr14,15 共LYP兲 correlation
functional 共B3LYP兲 with the 6-311+ G共d兲 basis set. To obtain improved energies, single point calculations have been
performed at the B3LYP/ 6-311+ G共d兲 equilibrium geometries, using the coupled cluster with single, double and perturbative triple excitations 关CCSD共T兲兴 method.16 Calculations were also carried out with the larger 6-311+ G共3df兲
basis set which includes three d and one f polarization function on C and O and three f and one g polarization function
on V. At each optimized stationary point, a vibrational analysis was performed to determine its character 共minimum or
saddle point兲 and to evaluate the zero point vibrational energy correction at B3LYP/ 6 – 311+ G共d兲. For the transition
state structure optimizations, we used the Synchronous
transit-guided quasi-Newton17,18 共STQN兲 method. These calculations were carried out with the GAUSSIAN 03 package.19
Geometries calculated at the B3LYP/ 6 – 311+ G共d兲 level
are quite good. For example, calculated re = 1.538 Å for VO+
compared to experiment ro = 1.561± 0.002 Å 共Ref. 20兲 and
C–O bond lengths of 1.128 Å in CO and 1.161 Å in CO2
agree with experiment to 0.001 Å. The V+共OCO兲 ground
state is calculated to be 5⌬, with bond lengths of 2.116 Å
共V – O1兲, 1.178 Å 共O1 – C兲, and 1.142 Å 共C – O2兲. Binding to
V+ lengthens the adjacent C–O bond by 0.017 Å and shortens the distant bond by a similar amount. Orbitals and electronic occupancies are shown in Fig. 4. The 5␲, 13␴, 1␦, and
14␴ are primarily 3d and 4s vanadium orbitals.
To evaluate the reliability of the B3LYP and CCSD共T兲
energies we compare calculated and experimental excitation
energies of V+ and bond dissociation energies for several
vanadium compounds 共Table I兲. All energies are calculated at
the B3LYP/ 6-311+ G共d兲 geometry and include zero point
energy at the B3LYP/ 6-311+ G共d兲 level. The splitting between the ground 共 5D , 3d4兲 and lowest triplet 共 3F , 3d34s1兲
states of V+ is fairly well reproduced by B3LYP calculations.
Our B3LYP results are very similar to those Sicilia and
Russo obtained with B3LYP/DZVP and B3LYP/TZVP.21 The
calculated CCSD共T兲 splitting is too low and is strongly dependent on the basis set. Several groups have calculated
D0共V+ – O兲 using density functional theory as well as
CCSD共T兲, complete active space self consistent field
共CASSCF兲, multiconfiguration self consistent field 共MCSCF兲, multireference average coupled-pair functional 共MRACPF兲, multireference singles and doubles configuration interaction 共MR-SDCI兲, and multireference second order
Møller-Plesset 共MRMP兲.22–26 Our DFT and CCSD共T兲 results
agree with the earlier values, but the calculated values are
consistently lower than experiment.20,27–31 A recent multireference average coupled-pair functional 共MR-ACPF兲 study
obtained a value of 5.98 eV for D0共V+ – O兲, but this required
developing very large correlation consistent basis sets and
extrapolating to the basis set limit.22 Accurately reproducing
the quintet-triplet splitting and VO+ bond strength with
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024307-5
J. Chem. Phys. 128, 024307 共2008兲
Mode selective photodissociation dynamics
FIG. 4. 共Color online兲 Molecular orbitals and electron occupancy of quintet
V+共OCO兲 共 5⌬兲 calculated at the B3LYP/ 6-311+ G共3df兲 level.
CCSD共T兲 will likely require substantially larger basis sets
than are currently practical for V+共OCO兲 and its isomers.
Calculated values for D0共V+ – OCO兲 and D0共OV+ – CO兲 are
in excellent agreement with the guided ion beam
experiments,31 particularly the CCSD共T兲 results; they also
show a much smaller dependence on basis set than
D0共V+ – O兲.
Figure 5 shows the calculated potential energy surface
for the V+ + CO2 reaction at the CCSD共T兲 / 6-311+ G共3df兲
level. Energies calculated with the smaller basis set and at
the B3LYP level are also shown in Table II and the geometries of stationary points are in Table III. As noted earlier,
the energies of the minima have been calculated previously,
but this is the first calculation of the barrier to insertion. The
global minimum of the PES is the triplet state of OV+CO
共Min2兲. This agrees with the calculation of Sodupe et al.2
and with the guided ion beam experiment,31 which places
triplet OV+CO 0.84± 0.14 eV below quintet V+共OCO兲. Our
calculations predict that there is a barrier for V+ 共 5D兲 to react
with CO2 to produce VO+ 共 3兺兲 + CO. Calculations with the
larger basis set predict a smaller barrier, so the size of the
barrier is likely not converged with respect to basis set. The
prediction of a barrier to reaction agrees with a recent selected ion flow tube 共SIFT兲 study32 which finds that V+ does
not react with CO2 at thermal energies. Earlier guided ion
beam 共GIB兲 experiments31 found that V+ reacts with CO2 at
low collision energy and that the reaction cross section drops
with collision energy, indicating a reaction with no barrier.
However, the SIFT results suggest that the VO+ observed in
the GIB experiments may have been due to trace O2 impurity, a possibility also raised in the original paper.31 Guided
ion beam experiments find that collisions of V+共OCO兲 with
Xe lead exclusively to V+, with no VO+ observed at collision
energies below 9 eV and VO+ / V+ ratios below 0.03 at
higher energies. The small amount of VO+ product is in
sharp contrast to what is found in the photodissociation studies, where VO+ / V+ ⬎ 0.3 throughout the visible band. The
reasons for this difference in reactivity will be explored, using the calculations described above of stationary points on
the potential energy surfaces for the reaction, as well as calculations of excited quintet and triplet states.
Our studies of the vibrational and electronic spectroscopy of V+共OCO兲 probe the ground state of the molecule, as
well as two excited electronic states, at ⬃6000 and
⬃15 800 cm−1, respectively.1 We have used time-dependent
density functional theory 共TD-DFT兲 to calculate excited
electronic states of V+共OCO兲. Calculations of excited electronic states of coordinatively unsaturated transition metal
systems are challenging, due to the large number of lowlying electronic states. In general, TD-DFT gives excitation
energies for transitions involving valence states with surpris-
TABLE I. Calculated and experimental excitation energy and bond dissociation energies for vanadium containing systems. All values are in eV. Calculations are single-point energies at the optimized B3LYP/ 6-311
+ G共d兲 geometry and include zero point energy at the B3LYP/ 6-311+ G共d兲 level.
B3LYP
Property
V 共 F − D兲
D0共V+ – O兲
D0共V+ – OCO兲
D0共OV+ – CO兲
+ 3
5
CCSD共T兲
6-311+ G共d兲
6-311+ G共3df兲
6-311+ G共d兲
6-311+ G共3df兲
Experiment
0.94
5.51
0.94
1.08
0.93
5.63
0.95
1.13
0.44
5.22
0.74
0.93
0.56
5.52
0.75
0.99
1.08a
5.85± 0.15,b 5.99± 0.09c
0.75± 0.04d
1.05± 0.10d
Averaged over spin-orbit levels 共Ref. 34兲.
References 26–28.
c
Based on D0共V+ – O兲 = D0共V – O兲 + IE共V兲 − IE共VO兲 共Refs. 19 and 29兲.
d
Reference 30.
a
b
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024307-6
J. Chem. Phys. 128, 024307 共2008兲
M. Citir and R. B. Metz
FIG. 5. 共Color online兲 Calculated potential energy surface for the V+
+ CO2 reaction. Energies are at the
CCSD共T兲 / 6-311+ G共3df兲 level, at the
B3LYP/ 6-311+ G共d兲 geometry and
include zero point energy at the
B3LYP/ 6-311+ G共d兲 level.
ingly good accuracy,33,34 providing an efficient alternative to
sophisticated wave function based approaches.
As V+共OCO兲 is an electrostatically bond complex, its
electronic states can be correlated to those of V+, so we first
perform TD-DFT calculations to evaluate the ability of different functionals 共B3LYP, B3PW91, B3P86, B98, BHandHLYP兲 and basis sets 共6-311+ G共d兲, 6-311+ G共3df兲, CEP121G, TZVP, SDD兲 to accurately predict excited states of
V+. Experimentally, V+ has a 5D ground state, with a 3d4
electronic configuration. The two lowest excited quintet
states are 3d34s 共 5F兲 at 0.34 eV and 3d34s 共 5 P兲 at 1.67 eV
共energies are the weighted average of spin-orbit states兲.35 All
of the functionals tested give an excitation energy for the 5 P
state that is too low, and several split the 5F into nondegenerate states. Results are given in Table S2 of Ref. 8.
Overall, the BHandHLYP functional with the 6-311
+ G共3df兲 basis set performed best, predicting the 5F state at
0.48 eV and 5 P at 1.34 eV and we used it for subsequent
calculations on V+共OCO兲. The optimized geometry of quintet V+共OCO兲 with BHandHLYP/ 6-311+ G共3df兲 is
r共V – O1兲 = 2.114 Å, r共O1 – C兲 = 1.163 Å, and r共C – O2兲
= 1.126 Å, which is very similar to the B3LYP/ 6-311
+ G共d兲 geometry. We then performed TD-DFT calculations
on quintet and triplet V+共OCO兲. The resulting adiabatic potential curves along the V+ – 共OCO兲 stretch are shown in Fig.
6. At each V+ – 共OCO兲 distance r共V – O1兲, all other bond
lengths are optimized for the ground state of the linear complex, for each spin state. We also carried out TD-DFT calculations to study the potential for the V+ – 共OCO兲 rock. We fix
the V–C bond length and the geometry of the OCO ligand to
their values at the quintet minimum and scan the V – O1 – C
angle 共␪兲 from 0° to 90° 共Fig. 7兲. Focusing first on the quintet states in Fig. 6 共shown with symbols兲, the three lowest
states correlate to ground state V+ 共3d4 , 5D兲. Interaction with
the ligand causes the degenerate atomic state to split into 5⌬,
5
兺, and 5⌸ states, based on the orientation of the unoccupied
d orbital 共see Fig. 4兲. All three states have a minimum at
r共V – O1兲 = 2.11– 2.16 Å, with a linear equilibrium geometry.
The next two quintet states correlate to V+ 共3d34s , 5F兲. They
are more weakly bound, and have longer metal-ligand bond
lengths r共V – O1兲 ⬇ 2.5 Å. This is to be expected, as V+ states
with a 4s electron will have weaker electrostatic binding, due
to repulsion between the ligand and the 4s electron. Transitions to one or both of these states are responsible for the
photodissociation we previously observed1 from 6050 to
TABLE II. Energies of stationary points on the V+ + CO2 potential energy surface calculated using the B3LYP
and CCSD共T兲 methods. All energies are in eV, relative to V+共 5D兲 + CO2. Single point energies are calculated at
the optimized B3LYP/ 6-311+ G共d兲 geometry and include zero point energy at the B3LYP/ 6-311+ G共d兲 level.
B3LYP
Species
V+共 5D兲 + CO2共 1⌺+兲
V+共 3F兲 + CO2共 1⌺+兲
V+共OCO兲, Min1 共 5A⬙兲
V+共OCO兲, Min1 共 3A⬘兲
TS 共 5A⬙兲
TS 共 3A⬙兲
OV+共CO兲, Min2 共 5A⬙兲
OV+共CO兲, Min2 共 3A⬙兲
VO+共 5⌺兲 + CO共 1⌺−兲
VO+共 3⌺兲 + CO共 1⌺−兲
CCSD共T兲
6-311+ G共d兲
6-311+ G共3df兲
6-311+ G共d兲
6-311+ G共3df兲
0.00
0.94
−0.94
−0.10
1.74
0.81
1.50
−1.12
2.74
−0.03
0.00
0.92
−0.95
−0.13
1.67
0.71
1.46
−1.15
2.73
−0.02
0.00
0.44
−0.74
−0.43
1.79
0.99
1.46
−1.24
2.59
−0.31
0.00
0.56
−0.75
−0.37
1.76
0.86
1.50
−1.19
2.70
−0.20
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024307-7
J. Chem. Phys. 128, 024307 共2008兲
Mode selective photodissociation dynamics
TABLE III. Calculated B3LYP/ 6-311+ G共d兲 geometries of the V+共OCO兲 and OV+共CO兲 minima, and of the
transition state between them, for the lowest quintet and triplet states. Bond lengths 共R兲 in Å and angles 共⬔兲 in
degrees.
Structure
State
Min1
Min1
Min2
Min2
TS
TS
Quintet
Triplet
Quintet
Triplet
Quintet
Triplet
R共V – O1兲
R共O1 – C兲
R共C – O2兲
R共V – C兲
⬔V – O1 – C
⬔O1 – C – O2
⬔O1 – V – C
2.116
2.096
1.844
1.543
1.825
1.731
1.178
1.178
2.922
3.022
1.959
1.467
1.142
1.141
1.118
1.117
1.123
1.152
3.294
3.274
2.207
2.214
2.192
1.978
180.0
180.0
49.0
44.9
70.7
75.9
180.0
180.0
138.4
143.5
124.8
134.5
¯
¯
91.8
105.7
57.5
46.0
⬎ 7400 cm−1. The V+ – OCO stretching frequency in this
band is observed to be 107 cm−1, significantly lower than for
the ground state 共210 cm−1兲, consistent with the calculations.
Figure 7 shows that at the V+ – C bond length in the ground
state, the ligand rotates to reduce the V+ – O repulsion. The
nearly flat rocking potential calculated for these states is consistent with a 25 cm−1 vibrational progression observed in
the photodissociation spectrum and tentatively assigned to
the metal-ligand rock.1 The highest-energy quintet state
shown correlates to V+ 共 5 P , 3d34s兲, and it is the state observed in the visible, near 15 800 cm−1. As expected from the
electron configuration, its V+ – OCO stretching and bending
potentials are similar to those of the near-IR states. The equilibrium V–O bond length is ⬇2.45 Å. At the V+ – C bond
FIG. 6. 共Color online兲 Adiabatic potential energy curves along the
V+ – 共OCO兲 stretch from TD-DFT calculations at the BHandHLYP/ 6-311
+ G共3df兲 level. Quintet states are shown with lines and symbols and triplet
states with lines. At each V+ – 共OCO兲 distance, r共V – O1兲, all other bond
lengths are optimized for the ground state of the linear complex, for each
spin state.
FIG. 7. 共Color online兲 Potential energy curves along the rocking coordinate
for V+共OCO兲. Quintet states are shown with lines and symbols and triplet
states with lines. As the V – O1 – C angle 共␪兲 is scanned from 0° to 90°, the
V–C bond length and the geometry of the OCO ligand are fixed at their
values at the quintet minimum.
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024307-8
J. Chem. Phys. 128, 024307 共2008兲
M. Citir and R. B. Metz
length of the ground state, the ligand also rotates away from
linearity. This is consistent with the observation of progressions in the V+ – OCO stretch 共186 cm−1兲 and rock
共105 cm−1兲 in the photodissociation spectrum. Overall, the
TD-DFT calculations of the quintet states of V+共OCO兲 do an
excellent job of predicting the observed photodissociation
spectrum. Modeling the dissociation dynamics, in which
VO+ 共 3兺兲 + CO is a major product, requires characterizing
triplet states of V+共OCO兲 and their coupling to the quintet
states.
The lowest triplet state of V+ is 3F 共3d34s兲, which is
calculated to lie 0.56 eV above the quintet ground state, and
there are several excited triplet states that lie nearby, including one other 3d34s state and four 3d4 states within about
1 eV.35 The short bond lengths and linear minima for the
lowest triplet states of V+共OCO兲 suggest that these states
arise from 3d4 configurations of V+. As shown in Figs. 6 and
7, calculations predict that there are several triplet states that
lie near 共and even cross兲 the excited quintet states. Because
several triplet states at similar energies are involved, we expect this general picture to be correct, despite the limited
accuracy of TD-DFT calculations.
Dissociation of excited quintet states of V+共OCO兲 to
produce VO+共 3F兲 + CO共 1兺兲 requires spin-orbit coupling of
quintet states to triplet states. Calculations by Rue et al.
looked at coupling between quintet and triplet states of the
isoelectronic V+共CS2兲 system.36 They argued that the main
contribution to the spin-orbit coupling is from the heavy atoms and used calculations on VS+ to estimate the spin-orbit
coupling in V+共CS2兲. To estimate the spin-orbit coupling,
calculations were carried out for VO+ at several different
bond lengths, and for V+共OCO兲 at the Min1 triplet geometry.
The GAMESS 共Refs. 37 and 38兲 package was used for the
spin-orbit calculations.39 The calculations consist of a restricted open-shell Hartree-Fock calculation on the triplet
state, using the 6-31G basis set on all atoms. The lowest
triplet and quintet states are calculated separately using the
complete active space 共CASSCF兲 method, with an active
space consisting of the 4s and 3d on vanadium and 2s and 2p
on oxygen. Excited quintet and triplet states are calculated
using configuration interaction 共CI兲 based on the CASSCF
states.40 Spin-orbit coupling between the CI states is calculated using the full two-electron Pauli-Breit operator, with
effective nuclear charges Zeff = 10.5, 6.0, and 3.9 for V, O,
and C, respectively.36
Calculated coupling between excited quintet and triplet
states ranges from ⬃10 to ⬃ 90 cm−1 for VO+ at r
= 1.543 Å, decreasing slightly to ⬃10 to ⬃ 70 cm−1 at
2.096 Å, where the range given reflects the fact that different
excited triplet states have differing couplings. Calculations at
2.096 Å using the larger 6-311+ G共3df兲 basis set on all atoms give slightly lower couplings of ⬃10– 65 cm−1. All calculations on V+共OCO兲 were carried out at the optimized
Min1 triplet geometry, which has r共V-O1兲 = 2.096 Å. This is
very similar to the Min1 quintet geometry. The active space
consists of the 4␲, 5␲, 13␴, 1␦, and 14␴ molecular orbitals,
as shown in Fig. 4. Spin-orbit couplings between excited
quintet and triplet states are calculated to be ⬃10– 140 cm−1
with the 6-31G basis and ⬃10– 90 cm−1 with the 6-311
+ G共3df兲 basis. At the same V-O bond length, the calculations predict slightly larger spin-orbit coupling for V+共OCO兲
than for VO+, although this may be due to using different
active spaces in the two cases.
Our results show that spin-orbit coupling in V+共OCO兲 is
slightly larger than for VS+ 共⬃20 cm−1兲,36 but is still weak
for most states and moderate41 for a few states. This helps to
explain why collisional excitation31 of V+共OCO兲 leads to
V+ + CO2 rather than spin-forbidden VO+ + CO. Collisional
excitation gives a statistical distribution of states.42 At moderate total energies, the vibrational densities of states in the
ground and low-lying quintet states are much higher than in
the triplet state, which lies at significantly higher energy. So,
low- and moderate-energy collisional excitation should overwhelmingly produce quintet V+共OCO兲. For quintet
V+共OCO兲, breaking the weak V+ – OCO bond is spin allowed
and has a loose transition state. In contrast, producing VO+
共 3兺兲 requires intersystem crossing to the triplet state, followed by isomerization over a tight transition state 共Fig. 5兲.
A small amount of VO+ is observed at collision energies over
8 eV, comprising 3% of the product at 20 eV. This may be
due to production of quintet VO+ 共 5兺兲 + CO, which lies
3.5 eV above V+共OCO兲, based on our calculation.
Photodissociation of V+共OCO兲 in the near-IR produces
only V+. This is likely because the lowest transition state to
insertion is calculated to lie 1.61 eV 共12 985 cm−1兲 above
quintet V+共OCO兲, which is significantly higher than the
6050– 7450 cm−1 excitation energy for the near-IR band.1
In contrast, photoexcitation of V+共OCO兲 in the visible
produces electronically excited quintet state molecules which
survive for many vibrational and even rotational periods, as
evidenced by the clearly resolved structure in the photodissociation spectrum. Several vibrational features are
⬍3.5 cm−1 wide, with unresolved rotational structure contributing to this width, indicating lifetimes of ⬎1.4 ps. The
slow internal conversion permits nonstatistical dynamics,
which lead to the observed mode selectivity.
We can use a simple model to estimate the branching
ratio between the reactive and nonreactive channels. The initially photoexcited quintet V+共OCO兲 can undergo internal
conversion, producing vibrationally excited, lower-lying
quintet states, or, via intersystem crossing 共ISC兲, it can form
triplet states. On the lowest quintet surface, production of
V+ + CO2 is favored, as it occurs over a lower barrier and via
a loose transition state. On the lowest triplet surface, the
reactive and nonreactive channels have similar barriers. In
this simple model, if an initially excited state has a large
intersystem crossing rate kISC, then it is more likely to form
the reactive VO+ product. We can calculate, approximately,
the intersystem crossing rate kISC using the “Golden Rule”
expression43
kISC =
2␲ 2
v ␳ f 共E兲,
ប ISC
where ␳ f 共E兲 is the density of states in the final 共triplet兲 state
at energy E and we assume that direct spin-orbit coupling
dominates the intersystem crossing rate, so
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024307-9
J. Chem. Phys. 128, 024307 共2008兲
Mode selective photodissociation dynamics
vISC = 具␺3兩HSO兩␺5典具␹3兩␹5典.
The first term is the spin-orbit coupling constant which we
calculated, and we ignore the variation of spin-orbit coupling
with geometry. The second term is the overlap of the initially
excited quintet state vibrational wavefunction with each triplet vibrational state at nearby energy. This term is responsible
for the mode selectivity in the intersystem crossing rate, and
hence in the photodissociation. Calculated kISC are convoluted with a 100 cm−1 full width at half maximum 共FWHM兲
Lorentzian to average over uncertainties in relative energies
due to vibrational anharmonicity and the relative energies of
the quintet and triplet states. To compute the vibrational
overlap integral, we assume that the vibrations are harmonic
and separable; the multidimensional overlap integral is then
the product of one-dimensional overlaps along each vibration. All vibrations are included; the vibrational frequencies
for the excited quintet state are the experimental values,1 the
frequencies for the triplet state are assumed to be those calculated for the lowest triplet state at the B3LYP/ 6-311
+ G共d兲 level. Displacements along each normal mode are estimated as follows: the displacements between the ground
and excited quintet state are calculated by matching observed
intensities in the photodissociation spectrum 共Fig. 2兲 and the
displacement between the ground quintet state and the excited triplet state is assumed to be small 共see below兲. From
the spectrum, there is substantial displacement in the
V+ – OCO stretch, with smaller displacements in the bend
and rock, and very little displacement in the OCO stretches.
The observed progressions in the bend and rock, as well as
Fig. 7, indicate that there is coupling between the V+ – OCO
stretch and these vibrations, as the minimum energy geometries of the ground and excited quintet states are both calculated to be linear.
The initially excited quintet state can couple to several
triplet states. The minimum in the lowest triplet state of
V+共OCO兲 lies ⬃11 000 cm−1 below the minimum of the initially excited state and has a similar geometry to the ground
quintet state, as shown in Figs. 6 and 7. As a result of the
large energy gap and modest difference in geometry, the vibrational overlap integrals and kISC are calculated to be very
small. The vibrational overlaps are only substantial for states
within ⬃2500 cm−1 of the initially excited state. This is consistent with Fig. 2, which shows a Franck-Condon envelope
that extends for ⬃1400 cm−1 for the transition between the
ground and excited quintet states; calculated overlaps between excited triplet states and the excited quintet states
should show a similar range, as the excited triplet states have
similar geometries to the ground quintet state. For a triplet
state 2500 cm−1 below the quintet state, and assuming a spinorbit coupling constant of 50 cm−1, kISC ⬇ 108 s−1. Parameters used to calculate kISC are given in Table S3 of Ref. 8.
Excitation in the V+ – OCO stretch, ␯3⬘ increases the rate, especially for several quanta. The displacement between the
excited quintet and triplet states is mostly along the
V+ – OCO stretch, so it is not surprising that excitation in this
vibration enhances the vibrational overlap and promotes intersystem crossing.
Several trends in the calculated kISC 共listed in Table S1 of
Ref. 8兲 agree with our observations of the branching ratio. In
general, more quanta of ␯3⬘ increase the yield of the reactive
channel. This is not simply the result of increasing energy, as
the state with one quantum of OCO bend, ␯4⬘ is observed and
calculated to be substantially less reactive than 3␯3⬘ and 3␯3⬘
+ ␯5⬘, which bracket its energy. Exciting the OCO antisymmetric stretch ␯1⬘ is also calculated to increase kISC, especially
when combined with exciting ␯3⬘, in accord with experiment.
This is due to two effects. The density of states increases
with energy, and exciting ␯1⬘ 共especially in combination with
␯3⬘兲 increases the vibrational overlap.
The calculations do not reproduce all of the experimental
observations. First, the calculations predict that exciting any
vibration enhances the reactivity. Experimentally, states with
one quantum of ␯3⬘ and one quantum of ␯4⬘ are less reactive
than the vibrational ground state. Also, the calculations predict large enhancements in kISC, by a factor of ⬃40 for states
with several quanta of ␯3⬘ and by a factor of ⬃120 for these
states in combination with ␯1⬘. This is much larger than the
observed range of reactivities. Also, the calculations predict
mode selectivity for quite highly vibrationally excited states,
while, experimentally, states at higher energies tend to have
similar reactivities. There are several possible reasons for
these discrepancies. First, it is possible, by chance, for the
initially excited vibrational state to be nearly in resonance
with a state with good vibrational overlap. This leads to large
variations in calculated kISC, especially at low energies,
where the density of states of the triplet state is modest. In
the calculations, we smooth this out somewhat by averaging
calculated kISC over a 100 cm−1 FWHM Lorentzian. This
may, however, explain the surprisingly low observed reactivity of ␯3⬘—there may just happen to be few triplet vibrational
states at nearby energies. Vibrational mixing in the excited
quintet state, due to cross anharmonicity and intramolecular
vibrational distribution, may help to explain why there is less
mode selectivity observed at higher energies, as the initially
excited state may not be very pure. The overestimate of
mode selectivity in the calculations may also be due to not
considering intersystem crossing to other triplet states, as
well as to ignoring the effect of initially excited state on the
internal conversion rate, and not considering the competition
between production of VO+ and V+ in the triplet manifold.
Photodissociation of V+共OCO兲 in the visible is mode
selective, with excitation of the V+ – OCO stretch and, to a
lesser extent, V+ – OCO rock and OCO antisymmetric stretch
enhancing the yield of the reactive VO+ channel. The mechanism for this enhancement is fairly complex, as the calculations predict that producing VO+ requires intersystem crossing to the triplet surface, and the transition state to produce
VO+ is not linear. The V+ – OCO stretch and OCO antisymmetric stretch appear to enhance reactivity by increasing the
intersystem crossing rate, while the rock may increase the
VO+ yield on the triplet surface.
ACKNOWLEDGMENTS
We thank Dr. Jeremy Harvey for assistance with the
spin-orbit coupling calculations. Support for this work by the
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024307-10
National Science Foundation 共Grant No. CHE-0608446兲 is
gratefully acknowledged.
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See EPAPS Document No. E-JCPSA6-127-013747 for Table S1: positions, assignments, VO+ / V+ branching ratios, and calculated intersystem
crossing rates for one photon and vibrationally mediated photodissociation of V+共OCO兲; Table S2: calculated energies for V+ electronic states
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